Quadtree adaptive WW3

[RichardMGorman]

Is your feature request related to a problem? Please describe.
Accuracy and computing efficiency can be improved by allowing spatial resolution to vary over the domain, to apply finer resolution where the solution varies most rapidly. For example unstructured or SMC grids can allow higher resolution near the coast. But further gains can be made by allowing resolution to vary dynamically as the solution evolves, e.g. to give fine resolution near a tropical cyclone.

Describe the solution you'd like
This can be addressed by using an adaptive quadtree grid. In a "proof-of-concept" paper (Popinet, S.; Gorman, R.M., Rickard, G.J; Tolman, H.L. (2010). A quadtree-adaptive spectral wave model. Ocean Modelling 34: 36-49) we demonstrated how this can work. A quadtree grid is developed from a regular grid by successively refining selected cells into four quadrants, and/or coarsening the grid by reversing this process. This can be done repeatedly during the simulation by refining where some measure of spatial variability of the solution (e.g. curvature of the wave height field) is high, and coarsening where it is low.
Now I would like to implement this fully into the present version of WW3, updating what I started some 5 years ago (on a "qa1" branch).

Describe alternatives you've considered
Some features of the SMC and unstructured grid approaches can be applied: e.g. SMC has similar structure to a (static) quadtree grid, so some SMC methods (e.g. propagation schemes) can be applied. But as far as I am aware, no other adaptive method has been proposed for inclusion in WW3.

Additional context
Add any other context or screenshots about the feature request here.

[aronroland]

Dear Richard, I always loved your work with Popinet and I think it was groundbreaking, especially at that time.

Now what we are looking at is to have such a feature for the unstructured grids, which are coupled to flow models that are as well adaptive.